
where
\(\Gamma _{\rm ph}^{ \gamma } = - {\rm Im} \Sigma _ \gamma ( \mathbf {k}, E_{ \gamma ,  \mathbf {k}} - \mu )\) 
with \( \Sigma _ \gamma ( \mathbf {k}, E_{ \gamma ,  \mathbf {k}} - \mu )\) 
being a self-energy given by the e–p interaction.
The real part of the self-energy
can be neglected for doping at low concentrations. [1]}
The quantity \(\Gamma \)  comes from another self-energy by
the impurity scattering.
Note that \(\Gamma _{\rm ph}^ \gamma \)  does not depend on \(\Gamma \) ,
and that the ratio \(\Gamma _{\rm ph}^{ \gamma }/\Gamma \) 
is crucial to the determination of
the \(T\)  dependence of the conductivity.
The quantity \(\Sigma _ \gamma ( \mathbf {k}, \omega ) = \Sigma _ \gamma ( \mathbf {k}, i \omega _n)\) 
with \(i\omega _n \rightarrow \omega + 0\) 
is estimated as
[2]}
\(& & \Sigma _ \gamma ( \mathbf {k}, i \omega _n) = T \sum _m \sum _{ \mathbf {q}}\; |\alpha _q|^2\nonumber \\& &\times \frac{1}{i \omega _{n+m} - \xi _{ \gamma ,  \mathbf {k}+ \mathbf {q}}}\times \frac{2 \omega _{ \mathbf {q}}}{\omega _{m}^2 + \omega _{ \mathbf {q}}^2} \; ,\) 
